Probability of resistance evolution for exponentially growing virus in the host

Chemotherapy for tumor and pathogenic virus often faces an emergence of resistant mutants, which may lead to medication failure. Here we study the risk of resistance to evolve in a virus population which grows exponentially. We assume that infected cells experience a "proliferation event" of virus at a random time and that the number of newly infected cells from an infected cell follows a Poisson distribution. Virus starts from a single infected cell and the virus infection is detected when the number of infected cells reaches a detection size. Initially virus is sensitive to a drug but later acquires resistance by mutations. We ask the probability that one or more cells infected with drug-resistant virus exist at the time of detection. We derive a formula for the probability of resistance and confirm its accuracy by direct computer simulations. The probability of resistance increases with detection size and mutation rate but decreases with the population growth rate of sensitive virus. The risk of resistance is smaller when more cells are newly infected by viral particles from a single infected cell if the viral growth rate is the same.     

THE EFFECTS OF POPULATION BOTTLENECKS ON CLONAL INTERFERENCE, AND THE ADAPTATION EFFECTIVE POPULATION SIZE

Clonal interference refers to the competition that arises in asexual populations when multiple beneficial mutations segregate simultaneously. A large body of theoretical and experimental work now addresses this issue. Although much of the experimental work is performed in populations that grow exponentially between periodic population bottlenecks, the theoretical work to date has addressed only populations of a constant size. We derive an analytical approximation for the rate of adaptation in the presence of both clonal interference and bottlenecks, and compare this prediction to the results of an individual-based simulation, showing excellent agreement in the parameter regime in which clonal interference prevails. We also derive an appropriate definition for the effective population size for adaptive evolution experiments in the presence of population bottlenecks. This "adaptation effective population size" allows for a good approximation of the expected rate of adaptation, either in the strong-selection weak-mutation regime, or when clonal interference comes into play. In the multiple mutation regime, when the product of the population size and mutation rate is extremely large, these results no longer hold.     

Disease,population viability,and recovery of endangered Sierra Nevada bighorn sheep

Sierra Nevada bighorn sheep (Ovis canadensis sierrae) experienced a severe population decline after European settlement from which they have never recovered; this subspecies was listed as endangered under the United States Endangered Species Act (ESA) in 1999. Recovery of a listed species is accomplished via federally mandated recovery plans with specific population goals. Our main objective was to evaluate the potential impact of disease on the probability of meeting specific population size and persistence goals, as outlined in the Sierra Nevada bighorn sheep recovery plan. We also sought to heuristically evaluate the efficacy of management strategies aimed at reducing disease risk to or impact on modeled bighorn populations. To do this, we constructed a stochastic population projection model incorporating disease dynamics for 3 populations (Langley, Mono, Wheeler) based on data collected from 1980 to 2007. We modeled the dynamics of female bighorns in 4 age classes (lamb, yearling, adult, senescent) under 2 disease scenarios: 5% lower survival across the latter 3 age classes and persistent 65% lower lamb survival (i.e., mild) or 65% reduced survival across all age classes followed by persistent 65% lower lamb survival (i.e., severe). We simulated management strategies designed to mitigate disease risk: reducing the probability of a disease outbreak (to represent a strategy like domestic sheep grazing management) and reducing mortality rate (to represent a strategy that improved survival in the face of introduced disease). Results from our projection model indicated that management strategies need to be population specific. The population with the highest growth rate ( ; Langley; = 1.13) was more robust to the effects of disease. By contrast, the population with the lowest growth rate (Mono; = 1.00) would require management intervention beyond disease management alone, and the population with a moderate growth rate (Wheeler; = 1.07) would require management sufficient to prevent severe disease outbreaks. Because severe outbreaks increased adult mortality, disease can directly reduce the probability of meeting recovery plan goals. Although mild disease outbreaks had minimal direct effects on the populations, they reduced recruitment and the number of individuals available for translocation to other populations, which can indirectly reduce the probability of meeting overall, range-wide minimum population size goals. Based on simulation results, we recommend reducing the probability of outbreak by continuing efforts to manage high-risk (i.e., spatially close) allotments through restricted grazing regimes and stray management to ensure recovery for Wheeler and Mono. Managing bighorn and domestic sheep for geographic separation until Sierra Nevada bighorn sheep achieve recovery objectives would enhance the likelihood of population recovery. © 2011 The Wildlife Society.     

Estimating Incidence Rates from Population‐Based Case‐Control Studies in the Presence of Nonrespondents

In population‐based case‐control studies, it is of great public‐health importance to estimate the disease incidence rates associated with different levels of risk factors. This estimation is complicated by the fact that in such studies the selection probabilities for the cases and controls are unequal. A further complication arises when the subjects who are selected into the study do not participate (i.e. become nonrespondents) and nonrespondents differ systematically from respondents. In this paper, we show how to account for unequal selection probabilities as well as differential nonresponses in the incidence estimation. We use two logistic models, one relating the disease incidence rate to the risk factors, and one modelling the predictors that affect the nonresponse probability. After estimating the regression parameters in the nonresponse model, we estimate the regression parameters in the disease incidence model by a weighted estimating function that weights a respondent's contribution to the likelihood score function by the inverse of the product of his/her selection probability and his/her model‐predicted response probability. The resulting estimators of the regression parameters and the corresponding estimators of the incidence rates are shown to be consistent and asymptotically normal with easily estimated variances. Simulation results demonstrate that the asymptotic approximations are adequate for practical use and that failure to adjust for nonresponses could result in severe biases. An illustration with data from a cardiovascular study that motivated this work is presented.     

Autocorrelated environmental variation and the establishment of invasive species

Environmental parameters such as temperature and rainfall have a positively autocorrelated variance structure which makes it likely that runs of good or bad conditions will occur. It has previously been demonstrated that such autocorrelated environmental variance can increase the probability of extinction in small populations, in much the same way that increased variance without autocorrelation can increase extinction risk. As a result, it has also been suggested that positive autocorrelation will decrease the probability that a species will establish in a novel location. We suggest that describing the probability of invasion success as the probability of indefinite persistence may be an inappropriate definition of risk. Economic or ecological damage may be associated with a population that initially reaches high densities before going extinct in the new location. In addition, such populations may spread to new locations before extirpation. We use a modeling approach to examine the effect of positively autocorrelated conditions on the probability that small populations will reach large size before extinction. We find that where variance is high and the geometric mean of the population growth rate is low, autocorrelation increases the risk that a population will pass a an upper threshold density, even when extinction probability is unaffected. Therefore species classified as having low probability of invasion risk on the basis of population growth rates measured in low variance environments may actually have quite a substantial probability of establishing a large population for a period of time. The mechanism behind the effect is the disproportionate influence of short runs of good conditions initially following introduction.     

The Incidence of Coronary Heart Disease and the Population Attributable Fraction of Its Risk Factors in Tehran: A 10-Year Population-Based Cohort Study

Background

Data on incidence of coronary heart disease (CHD) is scarce in the Middle East and little is known about the contribution of known risk factors in this area.

Methods

The incidence of CHD and the effect of modifiable risk factors were explored in 2889 men and 3803 women aged 30–74 years in the population based cohort of the Tehran Lipid and Glucose Study, during 1999–2010. Average population attributable fraction (aPAF) was calculated for any risk factor using direct method based on regression model.

Results

The crude incidence rate in men was about twice that in women (11.9 vs. 6.5 per 1000 person-years). The aPAF of hypertension, diabetes, high total cholesterol and low-HDL cholesterol was 9.4%, 6.7%, 7.3% and 6.1% in men and 17%, 16.6%, 12% and 4.6% in women respectively. This index was 7.0% for smoking in men. High risk age contributed to 42% and 22% of risk in men and women respectively.

Conclusions

The incidence in this population of Iran was comparable to those in the US in the seventies. Well known modifiable risk factors explained about 40% and 50% of CHD burden in men and women respectively. Aging, as a reflection of unmeasured or unknown risk factors, bears the most burden of CHD, especially in men; indicating more age-related health care is required.     

Effect of population stratification on case-control association studies. I. Elevation in false positive rates and comparison to confounding risk ratios (a simulation study)

OBJECTIVES: This is the first of two articles discussing the effect of population stratification on the type I error rate (i.e., false positive rate). This paper focuses on the confounding risk ratio (CRR). It is accepted that population stratification (PS) can produce false positive results in case-control genetic association. However, which values of population parameters lead to an increase in type I error rate is unknown. Some believe PS does not represent a serious concern, whereas others believe that PS may contribute to contradictory findings in genetic association. We used computer simulations to estimate the effect of PS on type I error rate over a wide range of disease frequencies and marker allele frequencies, and we compared the observed type I error rate to the magnitude of the confounding risk ratio. METHODS: We simulated two populations and mixed them to produce a combined population, specifying 160 different combinations of input parameters (disease prevalences and marker allele frequencies in the two populations). From the combined populations, we selected 5000 case-control datasets, each with either 50, 100, or 300 cases and controls, and determined the type I error rate. In all simulations, the marker allele and disease were independent (i.e., no association). RESULTS: The type I error rate is not substantially affected by changes in the disease prevalence per se. We found that the CRR provides a relatively poor indicator of the magnitude of the increase in type I error rate. We also derived a simple mathematical quantity, Delta, that is highly correlated with the type I error rate. In the companion article (part II, in this issue), we extend this work to multiple subpopulations and unequal sampling proportions. CONCLUSION: Based on these results, realistic combinations of disease prevalences and marker allele frequencies can substantially increase the probability of finding false evidence of marker disease associations. Furthermore, the CRR does not indicate when this will occur.     

TB Incidence in an Adolescent Cohort in South Africa

Background

Tuberculosis (TB) is a major public health problem globally. Little is known about TB incidence in adolescents who are a proposed target group for new TB vaccines. We conducted a study to determine the TB incidence rates and risk factors for TB disease in a cohort of school-going adolescents in a high TB burden area in South Africa.

Methods

We recruited adolescents aged 12 to 18 years from high schools in Worcester, South Africa. Demographic and clinical information was collected, a tuberculin skin test (TST) performed and blood drawn for a QuantiFERON TB Gold assay at baseline. Screening for TB cases occurred at follow up visits and by surveillance of registers at public sector TB clinics over a period of up to 3.8 years after enrolment.

Results

A total of 6,363 adolescents were enrolled (58% of the school population targeted). During follow up, 67 cases of bacteriologically confirmed TB were detected giving an overall incidence rate of 0.45 per 100 person years (95% confidence interval 0.29–0.72). Black or mixed race, maternal education of primary school or less or unknown, a positive baseline QuantiFERON assay and a positive baseline TST were significant predictors of TB disease on adjusted analysis.

Conclusion

The adolescent TB incidence found in a high burden setting will help TB vaccine developers plan clinical trials in this population. Latent TB infection and low socio-economic status were predictors of TB disease.     

Light at night co-distributes with incident breast but not lung cancer in the female population of Israel

Recent studies of shift-working women have reported that excessive exposure to light at night (LAN) may be a risk factor for breast cancer. However, no studies have yet attempted to examine the co-distribution of LAN and breast cancer incidence on a population level with the goal to assess the coherence of these earlier findings with population trends. Coherence is one of Hill's "criteria" (actually, viewpoints) for an inference of causality. Nighttime satellite images were used to estimate LAN levels in 147 communities in Israel. Multiple regression analysis was performed to investigate the association between LAN and breast cancer incidence rates and, as a test of the specificity of our method, lung cancer incidence rates in women across localities under the prediction of a link with breast cancer but not lung cancer. After adjusting for several variables available on a population level, such as ethnic makeup, birth rate, population density, and local income level, a strong positive association between LAN intensity and breast cancer rate was revealed (p<0.05), and this association strengthened (p<0.01) when only statistically significant factors were filtered out by stepwise regression analysis. Concurrently, no association was found between LAN intensity and lung cancer rate. These results provide coherence of the previously reported case-control and cohort studies with the co-distribution of LAN and breast cancer on a population basis. The analysis yielded an estimated 73% higher breast cancer incidence in the highest LAN exposed communities compared to the lowest LAN exposed communities.     

Modelling the effect of treatment and behavioral change in HIV transmission dynamics

In this paper we analyze a model for the HIV-infection transmission in a male homosexual population. In the model we consider two types of infected individuals. Those that are infected but do not know their serological status and/or are not under any sort of clinical /therapeutical treatment, and those who are. The two groups of infectives differ in their incubation time, contact rate with susceptible individuals, and probability of disease transmission. The aim of this article is to study the roles played by detection and changes in sexual behavior in the incidence and prevalence of HIV. The analytical results show that there exists a unique endemic equilibrium which is globally asymptotically stable under a range of parameter values whenever a detection /treatment rate and an indirect measure of the level of infection risk are sufficiently large. However, any level of detection/ treatment rate coupled with a decrease of the transmission probability lowers the incidence rate and prevalence level in the population. In general, only significant reductions in the transmission probability (achieved through, for example, the adoption of safe sexual practices) can contain effectively the spread of the disease.     

Two measures of effective population size for graphs

Effective population size is a key parameter in population ecology because it allows prediction of the dynamics of genetic variation and the rate of genetic drift and inbreeding. It is important for the definition of "nearly neutral" mutations and, hence, has consequences for the fixation or extinction probabilities of advantageous and deleterious mutations. As graph-based population models become increasingly popular for studying evolution in spatially or socially structured populations, a neutral theory for evolution on graphs is called for. Here, we derive formulae for two alternative measures of effective population size, the variance effective and inbreeding effective size of general unweighted and undirected graphs. We show how these two quantities relate to each other and we derive effective sizes for the complete graph the cycle and bipartite graphs. For one-dimensional lattices and small-world graphs, we estimate the inbreeding effective size using simulations. The presented method is suitable for any structured population of haploid individuals with overlapping generations.     

Transmission dynamics of hepatitis E among swine: potential impact upon human infection

Background

Colic (abdominal pain) is a clinical condition of serious concern affecting the welfare and survival of donkeys at the Donkey Sanctuary in the UK. One of the most commonly reported causes is due to impacted ingesta in the large intestine ("impaction colic"). However little is known about the incidence of, or risk factors for, this condition. Here we describe the epidemiology of colic in donkeys, specifically impaction colic. We focus on temporal aspects of the disease and we identify environmental and management related risk factors for impaction colic in UK donkeys.

Results

There were 807 colic episodes in the population of 4596 donkeys between January 1^st 2000 and March 31^st 2005. The majority (54.8%) of episodes were due to a suspected or confirmed diagnosis of impaction of the gastrointestinal tract. The mortality risk for all colics (51.1%) was higher than reported in other equids. The incidence rate of all colics (5.9 episodes per 100 donkeys per year) and of impaction colic (3.2 episodes) was similar to that in horses. A retrospective matched case-control study of all impaction colics from January 2003 (193) indicated that older donkeys, those fed extra rations and those that previously suffered colic were at increased risk of impaction. Lighter body weight, musculo-skeletal problems, farm and dental disease were also significantly associated with a diagnosis of impaction colic.

Conclusion

To our knowledge this is the first study to estimate the incidence rate of colic in a large population of donkeys in the UK. In contrast to other equids, impaction was the most commonly reported cause of colic. We identified several risk factors for impaction colic. Increasing age, extra rations and previous colic are known risk factors for colic in other equids. Results support the hypothesis that dental disease is associated with impaction colic. Musculo-skeletal problems may be associated with colic for various reasons including change in amount of exercise or time at pasture. Other associated factors (weight and farm) are the subject of further research. Identification of risk factors for impaction colic may highlight high risk donkeys and may allow intervention strategies to be introduced to reduce the incidence of the disease.     

Determination of the spread of HIV from the AIDS incidence history

The relation between the incidence of HIV in the general population, the number of AIDS cases, and the incubation period for the disease is examined. The number of AIDS cases can be expressed in terms of a convolution integral over the incubation period distribution and the temporal history of HIV incidence. In order to determine the level of HIV incidence it is necessary to invert the convolution. In this manner, it is possible to determine the spread of HIV up to the present time from knowledge of the AIDS incidence history and the incubation period. We describe the inversion of the convolution in terms of a Laplace transform technique that is applicable for any given incubation period distribution. Substantial simplifications in the technique are found in the case of an Erlang distribution for the probability density. The spread of HIV infections in the United States is charted through 1988 using AIDS incidence data that are corrected for both the revised AIDS case definition and reporting time delays. The results are consistent with current estimates of the HIV incidence in the United States and show no evidence of saturation in the rate of new infections. Indeed, the rate of new infections still appears to be climbing as of that date. While the technique is unable to predict the future course of the epidemic, it may provide a useful benchmark for comparison with mathematical models of the epidemic. The techniques are conceptually applicable to diseases other than AIDS.     

Estimation of the Exposure of the UK Population to the Bovine Spongiform Encephalopathy Agent through Dietary Intake During the Period 1980 to 1996

Although the incidence of variant Creutzfeldt-Jakob disease (vCJD) has declined to 1 since 2012 in the UK, uncertainty remains regarding possible future cases and the size of the subclinical population that may cause secondary transmission of the disease through blood transfusion. Estimating the number of individuals who were exposed to the bovine spongiform encephalopathy (BSE) infectious agent and may be susceptible to vCJD will help to clarify related public health concerns and plan strategies. In this paper, we explore this estimate by describing the probability of potential exposure due to dietary intake throughout the BSE epidemic period from 1980 to 1996 as a stochastic Poisson process. We estimate the age- and gender-specific exposure intensities in food categories of beef and beef-containing dishes, burgers and kebabs, pies, and sausages, separating the two periods of 1980–1989 and 1990–1996 due to the specified bovine offal legislation of 1989. The estimated total number of (living) exposed individuals during each period is 5,089,027 (95% confidence interval [CI] 4,514,963–6,410,317), which was obtained by multiplying the population size of different birth cohorts by the probability of exposure via dietary intake and the probability of survival until the end of 2013. The estimated number is approximately doubled, assuming a contamination rate of . Among those individuals estimated, 31,855 (95% CI 26,849–42,541) are susceptible to infection. We also examined the threshold hypothesis by fitting an extreme-value distribution to the estimated infectious dose of the exposed individuals and obtained a threshold estimate of 13.7 bID₅₀ (95% CI 6.6–26.2 bID₅₀) (Weibull). The results provide useful information on potential carriers of prion disease who may pose a threat of infection via blood transfusion and thus provide insight into the likelihood of new incidents of vCJD occurring in the future.     

Binary regression for risks in excess of subject-specific thresholds

We describe models for binary valued data to be used to explain the incidence of disease given the level of a known risk factor. Every individual has an unobservable tolerance of the risk. Risk levels below the individual tolerance do not increase the disease incidence above the background, unexposed rate. We estimate parameters from both the tolerance distribution and the risk function for a large group of mice exposed to very low levels of a known carcinogen.     

Radiation dose associated with renal failure mortality: a potential pathway to partially explain increased cardiovascular disease mortality observed after whole-body irradiation

Whole-body and thoracic ionizing radiation exposure are associated with increased cardiovascular disease (CVD) risk. In atomic bomb survivors, radiation dose is also associated with increased hypertension incidence, suggesting that radiation dose may be associated with chronic renal failure (CRF), thus explaining part of the mechanism for increased CVD. Multivariate Poisson regression was used to evaluate the association of radiation dose with various definitions of chronic kidney disease (CKD) mortality in the Life Span Study (LSS) of atomic bomb survivors. A secondary analysis was performed using a subsample for whom self-reported information on hypertension and diabetes, the two biggest risk factors for CRF, had been collected. We found a significant association between radiation dose and only our broadest definition of CRF among the full cohort. A quadratic dose excess relative risk model [ERR/Gy(2) = 0.091 (95% CI: 0.05, 0.198)] fit minimally better than a linear model. Within the subsample, association was also observed only with the broadest CRF definition [ERR/Gy(2) = 0.15 (95% CI: 0.02, 0.32)]. Adjustment for hypertension and diabetes improved model fit but did not substantially change the ERR/Gy(2) estimate, which was 0.17 (95% CI: 0.04, 0.35). We found a significant quadratic dose relationship between radiation dose and possible chronic renal disease mortality that is similar in shape to that observed between radiation and incidence of hypertension in this population. Our results suggest that renal dysfunction could be part of the mechanism causing increased CVD risk after whole-body irradiation, a hypothesis that deserves further study.     

Estimates of Lifetime Risk of Occupational Fatal Injury from Age-Specific Rates

The lifetime risk of fatal workplace injury is a critical issue in the evaluation of occupational hazards. Recently, Fosbroke, Kisner, and Myers (1997) described a metric for working lifetime risk (WLTR) to determine the probability that a worker will die due to a work-related fatal injury in a year over a certain number of years of employment. This quantity was defined assuming that the annual rate of fatal injuries will be the same each year during employment. Recognizing the fact that annual fatal injury rates differ with the age of the worker along with other factors, modification of the definition of working lifetime risk is derived. We obtain the estimates of the lifetime risk using age-categorized annual fatality rates and derive an estimate of the standard error of the WLTR estimator and a confidence interval for the WLTR. We illustrate these calculations by estimating the lifetime risk for work-related fatal injuries for workers in four high risk industries: agriculture-forestry-fishing, mining, construction, and transportation public utilities. The estimates are based on employment data from the Bureau of Labor Statistics and an updated version of fatality data from the National Traumatic Occupational Fatalities surveillance system.     

A spatially explicit model for an Allee effect: why wolves recolonize so slowly in Greater Yellowstone

A reduced probability of finding mates at low densities is a frequently hypothesized mechanism for a component Allee effect. At low densities dispersers are less likely to find mates and establish new breeding units. However, many mathematical models for an Allee effect do not make a distinction between breeding group establishment and subsequent population growth. Our objective is to derive a spatially explicit mathematical model, where dispersers have a reduced probability of finding mates at low densities, and parameterize the model for wolf recolonization in the Greater Yellowstone Ecosystem (GYE). In this model, only the probability of establishing new breeding units is influenced by the reduced probability of finding mates at low densities. We analytically and numerically solve the model to determine the effect of a decreased probability in finding mates at low densities on population spread rate and density. Our results suggest that a reduced probability of finding mates at low densities may slow recolonization rate.